19. Exercises

The acceleration, \displaystyle a \displaystyle \text{m}{{\text{s}}^{-2}}, of the cyclist, at time \displaystyle t seconds is given by: \displaystyle a=1-\frac{t}{15} for \displaystyle 0\le t\le 15.

The cyclist travels along a straight road.

a) Given that the cyclist starts at rest, find an expression for the velocity cyclist at time \displaystyle t.

b) What is the speed of the cyclist after 15 seconds?

c) How far does the cyclist travel in the 15 seconds?

The acceleration, \displaystyle a \displaystyle \text{m}{{\text{s}}^{-2}}, at time \displaystyle t seconds of a particle, which moves along a straight line, is given by:

\displaystyle a=\frac{t}{25} .

a) Given that the initial velocity of the particle is 2 \displaystyle \text{m}{{\text{s}}^{-1}}, find an expression for the velocity of the particle.

b) Find the distance that the particle travels in the first 50 seconds of its motion.

A dragster starts at rest and experiences an acceleration that decreases uniformly from 8 \displaystyle \text{m}{{\text{s}}^{-2}} to zero over a period of 10 seconds. It moves along a straight race track.

a) Show that at time \displaystyle t seconds the acceleration, \displaystyle a \displaystyle \text{m}{{\text{s}}^{-2}} is given by:

\displaystyle a=8-\frac{8t}{10}.

b) Find the speed of the dragster when it stops accelerating at the end of the 10 seconds.

c) Find the distance that the dragster travels in the 10 seconds.