1. A particle is dropped from the top of a tower, and its height, $h$ metres, at time $t$ seconds is given by $$h = 40 - 4.9t^2$$
Draw a displacement time graph for the particle.
What is the height of the tower?
$40$
2. A particle has position $y$ after $t$ seconds given by $$y = 8t - 2t^2 + 4$$
Draw a displacement time graph for the particle.
What is the total distance travelled by the particle in 4 seconds?
$16$
3. An object accelerates uniformly from rest at a rate of 4 m s-2.
Draw a displacement time graph for the first 2 seconds.
How far has the object travelled in the 2 seconds?
$8$
4. Amy walks to school in the mornings. She walks at a speed of 5 km/h for 500 metres before stopping at a shop to buy some sweets. It takes her 6 minutes to buy the sweets, and then she continues to walk the rest of the way to school at the same speed. The school is 2 km away from her house in a straight line. Draw a distance time graph (with km and h as units) for her journey.
5. An object has a velocity of 10 m/s for 6 seconds, then 5 m/s for 4 seconds. Draw a displacement time graph for the object.
6. The position of a particle is given by $$x = 2 + t(t-2)$$
Draw a displacement time graph between 0 and 4 seconds.
Draw a velocity time graph between 0 and 4 seconds.
Displacement time graph is solid, velocity time graph is dashed
7. Given the velocity time graph below, find the total displacement of the particle from its original position.
$10$
8. Shown below is a displacement time graph for an object. Write down the range of times for which the particle is moving away from its original position.
Moving away between 0 and 2, and 3 and 5
9. Here is a velocity time graph for a particle.
Draw an acceleration time graph for the particle.
Find the total displacement of the particle.
$187.5$
10. The displacement time graph below shows the journey of an object. Draw the velocity time graph for the object.
11. An object has a displacement, $x$, over time, $t$, given by $$x = 4+3t^2-t^3$$ Draw the velocity time graph between $t=0$ and $t=2$.
12. Here is the acceleration time graph for a particle which starts at rest. Draw the displacement time graph for the particle.
