18. Exercises

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Exercise 18.1

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.

Answer a
Answer 18.1a
Answer b
Answer 18.1b
Answer c
Answer 18.1c
Solution a
Solution 18.1a
Solution b
Solution 18.1b
Solution c
Solution 18.1c


Exercise 18.2

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.


Answer a
Answer 18.2a
Answer b
Answer 18.2b
Answer c
Answer 18.2c
Solution a
Solution 18.2a
Solution b
Solution 18.2b
Solution c
Solution 18.2c
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