18. Exercises

As a car moves along a straight rod the distance, \displaystyle s metres, of a car from the origin at time \displaystyle t seconds is given by:

\displaystyle s=\frac{{{t}^{3}}}{3}-\frac{{{t}^{4}}}{60} for \displaystyle 0\le t\le 10.

a) By differentiating, find an expression for the velocity of the car at time \displaystyle t.

b) Find an expression for the acceleration of the car at time \displaystyle t.

c) Find the times when the acceleration of the car is zero.

A particle, of mass 4 kg, accelerates from rest so that the distance that it has travelled in \displaystyle t seconds is \displaystyle s where \displaystyle s=5{{t}^{2}}-6t.

a) Find the velocity and acceleration of the particle.

b) Find the time when the velocity is zero.

c) Find the magnitude of the resultant force on the particle at this time.

A crane lifts a load from ground level. The height, \displaystyle s m, of the lift at time \displaystyle t seconds is given by \displaystyle s=\frac{3{{t}^{2}}}{50}-\frac{{{t}^{3}}}{250} for \displaystyle 0\le t\le 10.

a) Show that the velocity of the load is zero when \displaystyle t=\text{ 1}0.

b) Find the height of the load at this time.

c) Find the time when the acceleration of the load is zero.

d) Find the height of the load at this time.