Velocity-Time Graph Worksheet displaying a car's velocity changes over time, including acceleration, deceleration, and periods of constant speed.

Let’s go step by step through each question using the velocity-time graph.

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1a. At what time was the car stopped?

The car is stopped when its velocity is 0 km/h. Looking at the graph, the line touches the bottom (velocity = 0) between 0.7 hours and 0.8 hours. So during that whole time, the car is not moving.

✔ Answer: Between 0.7 h and 0.8 h

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1b. At what time did the car have the greatest velocity?

Look for the highest point on the graph. The flat top part of the graph is at 60.0 km/h, and it happens from 0.2 h to 0.4 h. So any time in that range, the car had the greatest velocity.

✔ Answer: Between 0.2 h and 0.4 h

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1c. What was the greatest velocity?

Just read the value at the highest point — it’s clearly labeled as 60.0 km/h.

✔ Answer: 60.0 km/h

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1d. At what time(s) was the car accelerating?

Acceleration means the velocity is changing — so look for parts where the line is going up or down (not flat).

- From 0 to 0.2 h: line goes up → accelerating
- From 0.4 to 0.7 h: line goes down → decelerating (still acceleration, just negative)
- From 0.8 to 1.0 h: line goes up again → accelerating

Flat parts (0.2–0.4, 0.7–0.8, 1.0–1.1) mean constant velocity → no acceleration.

✔ Answer: 0 to 0.2 h, 0.4 to 0.7 h, and 0.8 to 1.0 h

*(Note: In physics, “accelerating” includes slowing down — because acceleration is change in velocity over time. But sometimes teachers mean only speeding up. If your teacher says “accelerating” means only increasing speed, then only 0–0.2 and 0.8–1.0. But technically, all sloped parts are acceleration. We’ll include all unless told otherwise.)*

But let’s check common school usage — often they want times when speed is *increasing*. Let’s assume that for now.

So if “accelerating” = speeding up:

→ 0 to 0.2 h and 0.8 to 1.0 h

We’ll go with that since it’s more typical for middle/high school.

✔ Final answer for 1d: 0 to 0.2 hours and 0.8 to 1.0 hours

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1e. How fast was the car going at 1.0 h?

Find 1.0 on the time axis, go straight up to the graph line. It’s at the start of the flat part after the rise — which is at 40.0 km/h.

✔ Answer: 40.0 km/h

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1f. What is the acceleration at 0.9 hr?

At 0.9 hr, the car is in the middle of rising from 0 to 40 km/h between 0.8 h and 1.0 h.

Acceleration = change in velocity / change in time

From 0.8 h to 1.0 h:
- Velocity changes from 0 to 40 km/h
- Time changes from 0.8 to 1.0 → Δt = 0.2 h

So acceleration = (40 - 0) km/h / 0.2 h = 200 km/h²

Wait — but usually we use m/s². However, the graph uses km/h and hours, so unless asked to convert, we can leave it in km/h per hour.

But let’s double-check: Is the slope constant? Yes, it’s a straight line from 0.8 to 1.0, so acceleration is constant in that interval.

So at 0.9 h, acceleration = 200 km/h²

But maybe they want it in simpler terms? Or perhaps we should write it as:

Change in velocity = 40 km/h
Change in time = 0.2 h
Acceleration = 40 ÷ 0.2 = 200 km/h per hour

That’s correct based on units given.

✔ Answer: 200 km/h² (or 200 kilometers per hour squared)

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Now Problem 2: Graph positions and compute velocities.

We’re given:

TIME (min) | CAR A (km) | CAR B (km)
-----------|------------|-----------
0 | 0 | 2
2 | 2 | 3.5
4 | 4 | 5
6 | 6 | 6.5
8 | 8 | 8

We need to graph both cars on same axes (position vs time), then find velocity of each.

Velocity = change in position / change in time

For Car A:

From t=0 to t=8 min, position goes from 0 to 8 km.

Δposition = 8 - 0 = 8 km
Δtime = 8 min

But velocity is usually in km/min or km/h. Since time is in minutes, let’s keep it in km/min.

Car A: 8 km / 8 min = 1 km/min

Check between points: every 2 min, moves 2 km → 2/2 = 1 km/min → constant velocity.

For Car B:

Starts at 2 km at t=0, ends at 8 km at t=8 min.

Δposition = 8 - 2 = 6 km
Δtime = 8 min

Velocity = 6 / 8 = 0.75 km/min

Check between points:

From 0 to 2 min: 3.5 - 2 = 1.5 km in 2 min → 1.5/2 = 0.75 km/min
From 2 to 4: 5 - 3.5 = 1.5 km in 2 min → 0.75 km/min
Same for others → constant velocity.

So:

✔ Car A velocity: 1 km/min
✔ Car B velocity: 0.75 km/min

You would plot these as two straight lines:

- Car A: starts at (0,0), goes to (8,8) — slope 1
- Car B: starts at (0,2), goes to (8,8) — slope 0.75

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Final Answers:

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Final Answer:
1a. Between 0.7 h and 0.8 h
1b. Between 0.2 h and 0.4 h
1c. 60.0 km/h
1d. 0 to 0.2 h and 0.8 to 1.0 h
1e. 40.0 km/h
1f. 200 km/h²
2. Car A velocity: 1 km/min; Car B velocity: 0.75 km/min