Describing Motion Around Us: questions with answers

A complete position gives the distance and the direction from a named reference point at one instant of time. Only 30 m east of the gate at 8:00 a.m. gives all three. The second choice leaves out the direction. The third names no reference point. The fourth gives a time interval of 5 minutes instead of one instant, and the bicycle can move during it.

An object is in motion when its position changes with respect to the chosen reference point. The passenger's position does not change with respect to the seat, so the passenger is at rest relative to the seat. The passenger's position does change with respect to the ground, so the passenger is in motion relative to the ground.

Total distance is 400 km and total time is 5 h, giving average speed 80 km/h. Returning to the start gives zero displacement and zero average velocity.

Average speed is total distance divided by total time taken. Average velocity is displacement divided by total time taken. The time denominator is the same, so only the numerators differ. Displacement has direction, so average velocity has direction too.

Distance is 100 + 60 = 160 m. Displacement is final position minus initial position: 40 − 0 = +40 m.

Returning to the starting point gives zero displacement. The ball travels one circumference, so its distance is 2πR.

During the first stage, acceleration is (15 − 5)/5 = 2 m/s². During the second stage, velocity stays constant, so acceleration is zero.

A sign tells us the direction, not whether the object speeds up or slows down. Here the velocity is negative and the acceleration is negative, so both point the same way. When velocity and acceleration point in the same direction, the object speeds up, so its speed increases.

Height represents position, so the object stays at 40 m. Slope represents velocity; the horizontal line has zero slope, so the object is at rest.

Slope on a position-time graph gives velocity. Both slopes are positive, and B has the larger slope, so B has greater speed. Both straight lines represent zero acceleration.

The height of the line gives the velocity, 20 m/s. The line is flat, so its slope, the acceleration, is zero. The area, 20 m/s × 6 s = 120 m, is the displacement, not an acceleration.

The velocity changes by 10 m/s − 5 m/s = 5 m/s. The time interval is 20 s − 10 s = 10 s, not the clock reading 20 s. Acceleration is 5 m/s ÷ 10 s = 0.5 m/s², and its unit is m/s², not m/s.

Use v² = u² + 2as with u = 0. Then s = 100/4 = 25 m; elapsed time is unnecessary.

For stopping, 0 = u² + 2as. With u = 20 m/s and a = −5 m/s², s = 40 m. Doubling speed quadruples stopping distance under the same constant braking acceleration.

The child travels along the whole circle, so the distance is the circumference 2πR. One full revolution ends at the starting point, so the displacement is 0. Average velocity is displacement divided by time, which gives 0 ÷ T = 0.