SPH3U Exam Practice Problems

Measurement, Unit Conversions, Significant Figures

  1. Gabe’s family car has an unconventional speedometer, displaying speed in metres per second. If Gabe goes for a joyride and drives 13.5 m/s, how fast is he going in km/h?(48.6 km/h)

Waves and Sound Unit

  1. Anna Maria falls through the ice on a cold winter day (-5 °C) and 400 m away from her sled dog team. Meanwhile, Jessica finds herself menaced by a Great White Loan shark while swimming in the Gulf of Mexico (30 °C), 400 m away from Laurenthe lifeguard. If both of them call for help, who will be heard first (by the sled dog team, or by the lifeguard), and how much faster will the cry arrive (in seconds)?(Jessica, by 0.073 s)
  1. Maude discovers an open-ended pipe that is 75 cm long, and, after beating off Cara and Cassandra for possession of it, decides that it would be perfect for making a wind instrument. Assuming a speed of sound of 344 m/s, what are the wavelengths and frequencies of the first 3 resonant modes for the tube? Sketch the resulting standing wave for each resonant mode. (1.5 m, 229 Hz; 0.75 m, 459 Hz; 0.5 m, 688 Hz)

Kinematics (Motion) Unit

  1. Elliot tests out his prototype stealth longboard, increasing speed smoothly from a stop to 15 m/s in just 10 s. (a) Sketch a velocity-time graph, and use this to also sketch position-time and acceleration-time graphs, and a motion map for his motion. Find values for and label on your graphs the following: initial and final velocities, initial and final positions, and acceleration (0 m/s, 15 m/s [fwd], 0 m, 75 m [fwd], 1.5 m/s2 [fwd]) . (b) Findhis displacement by using your velocity-time graph. (displacement is 75 m [fwd])
  1. Quinntonand Quincy discover one of Elliot’s abandoned earlier ideas, a stealth wheelchair, and are later observed slowing down smoothly from 15 m/s to 5 m/s at 2 m/s2. (a) How long does it take for them to reach their final velocity? (5 s) (b) Draw velocity-time, position-time and acceleration-time graphs for their motion, assuming that the position at which they begin slowing is the origin. (b) Find their displacement while slowing down by using your velocity-time graph. (displacement is 50 m [fwd])

Chase Problem

  1. A white mouse, starting 30 m [N] of its hole (the origin) scampers toward its hole at a constant velocity of 2.0 m/s [S]. A black cat, starting 60 m [N] of the hole, starts running at exactly the same time at a constant velocity of 5.0 m/s [S]. Using the mouse hole as the origin, sketch the position-time graphs and the velocity-time graphs for this wildlife drama (draw the position-time graphs for both cat and mouse coming all the way back to the hole). Use the velocity-time graph to determine the mouse’s displacement when the cat reaches the hole. (24 m [S])
  1. A rocket ship moving at 8285 m/s, in order to achieve stable orbit speed, needs to accelerate at 53.5 m/s2for 35.0 seconds.

a)How far does the rocket ship travel during that time?

b)What is the ship’s final speed? (Hint: do not use your answer from part a)

  1. Driving your race car at 135 km/h, you see a sharp curve up ahead. You know to take the corner safely you have to reduce your speed to 98 km/h; what must your acceleration be if the curve is 65 m away?
  1. You are watching a jet car attempt to break the land speed record. The car accelerates constantly from rest at 5.0m/s2, for a distance of 420 m. At what distance was its instantaneous speed equal to half its final speed?

Forces Unit

  1. You are pushing a 15kg object against the ceiling. If the normal force is 73.0N, what force are you pushing with?
  1. You are lifting a 15kg desk. If the normal force is 73.0N, what force are you pushing with?
  1. Two objects in orbit around Earth have the same mass. If object A is three times as far from Earth’s centre as object B, what is the ratio between the gravitational forces they experience due to Earth’s gravity (FA/FB = ?)?
  1. Some very nice sailors are using their boat to give three ducks a fun ride by pulling them along in the water. The boat exerts a 100.0 N pull force on the first duck, and a rope connects the first duck with the second. Another rope connects the third duck with the second. Assume no friction or air resistance in this problem (the ducks are very streamlined). Calculate the magnitude of the tension in the rope between the 7.0 kg duck and the 5.0 kg duck.
  1. Bill (75.0 kg) and Andrea (65.0 kg) are skating on their backyard pond. From a standstill, Andrea pushes Bill with a force of 32 N, and at the same time Bill pushes Andrea with a force of 25 N. What will Andrea’s motion be?

Work, Power & Energy Unit

  1. If a person pushes a box 5.0 m across a floor at constant speed, with a force of 250 N, how much work did they do?
  1. With a power rating of 345W, how far will a force of 115.0N push an object in 5.00s?
  1. How high would a 4.5 kg object go if you launched it straight up with an initial speed of 15.0 m/s (full marks must use energy!)?
  1. If a motor has an efficiency of 25%, how much energy will it require to produce 6550 J of work?
  1. If you pull a 12.0 kg desk 3.5 m across the room, with a 150.0 N force at an angle 25º up from the horizontal, how much work have you done on the desk?
  1. The brakes on a 1250 kg vehicle moving at 90.0 km/h exert 250 kJ of work on the vehicle over a distance of 30.0 m. The final speed is 54 km/h; what force did the brakes apply?
  1. A bicycle can have an efficiency (pedals to wheels) of 85%. Assuming this level of efficiency, how quickly can a cyclist with a power input of 655 W achieve a speed of 10.0 m/s? Assume no friction or air resistance, and that the bicycle and rider together have a mass of 85 kg.
  1. A 10.0 kg box slides down a frictionless ramp at 65º to the horizontal, from a height of 8.0 m. At the bottom, it slides horizontally until it comes to a complete stop. If the horizontal surface has a kinetic friction coefficient of 0.25, how far will the box slide?
  1. The motor on a 1250 kg vehicle moving at 25.0 km/h exert 250 kJ of work on the vehicle over a distance of 65.0 m. The final speed is 74 km/h; what force did the motor apply?
  1. A car engine is capable of delivering 53.5kW of power. If it changes the car’s speed from 18m/s to 25m/s over a distance of 25m, what force did it apply?