Which of the following velocity vs. time graphs corresponds to this position vs. time graph?

• A

• B

• C

• D

Answer explanation

The line is going up along the y-axis, which means its position is increasing; so its moving in the positive direction. Also, the line is curved upwards, meaning the position is increasing faster as time goes on. So the object is speeding up! Graph B is the only velocity vs time graph with a positive, increasing velocity.

Which equation best represent this position vs time graph?

• x_f = (5 m/s)t

• x_f = (5 m/s)t + 2.5 m

• x_f = (10 m/s)t

• x_f = (10 m/s)t + 2.5 m

Answer explanation

The graph has a slope of 5, and a y-intercept of 2.5 (you can see that it starts at the 2.5 mark on the vertical line). So it's equation must be:
x_f = (5 m/s)t + 2.5 m

The object's velocity in this graph is represented by:

• The y-intercept

• The area under the curve

• The slope

• Velocity cannot be determined from this graph

Answer explanation

The velocity of an object is its change in position over time. In a position vs time graph, position / time is the same as its y value divided by its x value; in other words, the slope.

1. If the graph represented a car moving in a straight line, which of the following best describes its motion?

• Moving at a constant velocity

• Moving at an increasing speed

• Moving at an increasing acceleration

• Not moving at all

Answer explanation

The slope is positive for this graph, so the car is moving in the positive direction over time. Since the line is straight, the velocity is constant; it's moving at a constant speed, not speeding up nor slowing down. Every 1 second it moves 5 meters.

From this plot, the acceleration of the car must be...

• Zero

• Constant but not zero

• Increasing

• Decreasing

Answer explanation

The slope of the line is a constant, positive number. So the car is moving in the positive direction at a constant speed. If speed is constant (unchanging), then acceleration is zero.

From this graph...

• The object is speeding up in the positive direction

• The object is speeding up in the negative direction

• The object is slowing down in the positive direction

• The object is slowing down in the negative direction

Answer explanation

The position is decreasing over time, so the object is moving in the negative direction. The line starts steep, but flattens out over time, so the object is slowing down.

From this graph...

• The object is speeding up in the positive direction

• The object is speeding up in the negative direction

• The object is slowing down in the positive direction

• The object is slowing down in the negative direction

Answer explanation

The position is increasing over time, so the object is moving in the positive direction. The line starts flat, but sharply rises over time, so the object is speeding up.

From this graph...

• The object is speeding up in the positive direction

• The object is speeding up in the negative direction

• The object is slowing down in the positive direction

• The object is slowing down in the negative direction

Answer explanation

The position is increasing over time, so the object is moving in the positive direction. The line starts steep, but flattens over time, so the object is slowing down

From this graph...

• The object is speeding up in the positive direction

• The object is speeding up in the negative direction

• The object is slowing down in the positive direction

• The object is slowing down in the negative direction

Answer explanation

The position is decreasing over time, so the object is moving in the negative direction. The line starts flat, but drops dramatically over time, so the object is speeding up

Which of the following objects is NOT accelerating?

• A ball dropped from a tall building

• A ball thrown straight up in the air

• A friction-negligible lab cart moving across a flat, friction-negligible desk

• A friction-negligible lab cart moving down an inclined ramp

Answer explanation

Without friction or gravity, a cart moving across a flat surface has no reason to slow down, speed up, or change direction. So it has ZERO acceleration.