PVA worksheet #2
For questions 1-6, the position of a particle moving along a straight line is given by s(t) = 2t 3 – 15t 2 + 36t – 36.
1.
The distance s is increasing for what values of t?
0 < t < 2 and t > 3
2.
The acceleration is positive for what values of t? t > 5/2
3.
The velocity of the particle is decreasing for what values of t?
0 < t < 5/2
4.
Find the velocity and speed at t = 2
Velocity is 0. Speed is 0
5.
The speed of the particle is decreasing for what values of t?
0 < t < 2 and 5/2 < t < 3
6.
Find the net displacement and total distance travelled of the particle from t = 0 to t = 4
Displacement is s(4) – s(0) = 32, total distance travelled = 34
7.
The position of a particle moving along a horizontal line at any time, t, is given by s(t) = t 2 – 2t – 15. For what value(s) of t is the particle not moving?
At t = 1
8.
A particle moves in a straight line such that its distance at time t from a fixed point on the line is given by 16t – 4t 2 units. What is the total distance travelled by the particle from t = 0 to t = 4?
32 units