19. Exercises
From Mechanics
| Theory | Exercises |
Exercise 19.1
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?
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Exercise 19.2
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.
Exercise 19.3
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.
Exercise 19.4
A car, of mass 1000 kg, accelerates for 20 seconds along a straight road. The graph below shows how the resultant force on the car varies with time as it accelerates.
a) Show that the acceleration, \displaystyle a \displaystyle \text{m}{{\text{s}}^{-2}}, at time \displaystyle t seconds is given by
\displaystyle a=\frac{4t}{5} for \displaystyle 0\le t\le 20.
b) Given that the velocity of the car is 8 \displaystyle \text{m}{{\text{s}}^{-1}}
when it starts to accelerate, find an expression for the velocity of the car at time \displaystyle t
seconds.
c) Find the distance travelled by the car in the 20 second period.
Exercise 19.5
A van slows down from a speed of 20 \displaystyle \text{m}{{\text{s}}^{-1}} to 5 \displaystyle \text{m}{{\text{s}}^{-1}} in 40 seconds. At time \displaystyle t seconds the acceleration, \displaystyle a \displaystyle \text{m}{{\text{s}}^{-2}} is given by \displaystyle a=-kt, where \displaystyle k is a constant.
a) Find \displaystyle k.
b) Find the distance that the car travels during the 40 seconds.
