Physics Practice Test: Kinematics and Motion Graphs

v = v₀ + at = 0 + 2.5 × 6.0 = 15 m/s. The value 45 is the distance traveled in meters (½at²), not the speed.

d = ½at² = ½ × 1.5 × 8.0² = 48 m. Forgetting the ½ gives 96 m, and 12 is the final speed in m/s.

From h = ½gt², t = √(2h/g) = √(2 × 44.1 / 9.8) = √9 = 3.0 s. Leaving out the factor 2 gives 2.1 s, and dividing 44.1 by 9.8 without the square root gives 4.5.

At the top v = 0, so h = v₀²/(2g) = 19.6² / 19.6 = 19.6 m. Forgetting the 2 in the denominator gives 39.2 m; 2.0 is the time to the top in seconds.

Velocity is the slope of the position-time graph: (20 m − 0 m) / (4 s − 0 s) = 5.0 m/s. The value 2.5 m/s is the average over the whole 8 s, and 20 is just the position reached.

The line is horizontal, so the position stays at 20 m and the slope (velocity) is zero. A horizontal line on a position-time graph never means constant nonzero speed; that would be a slanted line.

Acceleration is the slope of the velocity-time graph: 12 m/s ÷ 4 s = 3.0 m/s². The value 24 is the area under that part of the graph, which is a displacement in meters, not an acceleration.

Displacement is the area under the graph: triangle ½ × 4 × 12 = 24 m plus rectangle 6 × 12 = 72 m, total 96 m. Using 12 m/s for all 10 s gives 120 m, which ignores the speeding-up phase.

Average velocity is displacement divided by time, and her displacement is zero because she ends at the starting point. Her average speed is 400 m ÷ 80 s = 5.0 m/s, but speed and velocity are different quantities.

With uniform deceleration the average speed is (24 + 0)/2 = 12 m/s, so d = 12 × 4.0 = 48 m. Multiplying the initial speed by the time gives 96 m, as if the car never slowed down; 6.0 is the deceleration in m/s².

The fall time depends only on the height: t = √(2 × 1.225 / 9.8) = 0.50 s. The horizontal distance is 3.0 m/s × 0.50 s = 1.5 m. The value 0.50 is the time, not a distance.

Gravity acts during the whole flight, so the acceleration is always 9.8 m/s² downward. At the top only the vertical part of the velocity is zero; the horizontal part is unchanged, so the velocity is not zero.

Slope = change in velocity ÷ change in time, which is the definition of acceleration. Displacement is the area under a velocity-time graph, not its slope.

First convert: 72 km/h ÷ 3.6 = 20 m/s. Then t = 500 m ÷ 20 m/s = 25 s. Dividing 500 by 72 without converting units gives 6.9 s.

When velocity and acceleration point the same way, the object speeds up, whatever the sign. A negative acceleration means slowing down only when the velocity is positive.