A constant force F = 100 N acts on a body of mass m = 5 kg…

A constant force $F = 100\ \mathrm{N}$ acts on a body of mass $m = 5\ \mathrm{kg}$, initially at rest, for the time shown in Figure III. (a) What is the acceleration while the force acts? (b) What speed does the body reach? (c) Draw the velocity and acceleration diagrams.

Explanation of Method

A constant force acting for a limited time.

Step 1: (a) Acceleration

\[ a = \frac{F}{m} = \frac{100}{5}. \]

\[a = 20\ \mathrm{m/s^2} \ \text{while the force acts, then } 0\]

Step 2: (b) Final speed

If the force acts for a time $\tau$ (read from Figure III): $v = a\tau = 20\,\tau\ \mathrm{m/s} \ \ (\tau \text{ in seconds})$.

For example, a force lasting 2 s would give 40 m/s.

Step 3: (c) Diagrams

The acceleration is a horizontal line at 20 m/s² up to $\tau$ and zero afterwards. The velocity is a straight line $v = 20t$ up to $\tau$, then stays constant at $20\tau$, since no force acts any more (no friction).

$a\ (\mathrm{m/s^2})$ $t$ $20$ $v\ (\mathrm{m/s})$ $t$ $\tau$ $\tau$ $v = 20t$ $v = 20\tau$ $a = 20\ \mathrm{m/s^2}$

While the force acts (until $\tau$, read from Figure III), the acceleration is a constant 20 m/s² and the speed grows linearly. After that the acceleration drops to zero and the speed stays at $20\tau$.

Result

\[\boxed{\,a = 20\ \mathrm{m/s^2} \ \text{while the force acts, then } 0\,}\]

\[\boxed{\,v = a\tau = 20\,\tau\ \mathrm{m/s} \ \ (\tau \text{ in seconds})\,}\]

Remark

Note. The original result $a = 20\ \mathrm{m/s^2}$ is correct. The duration is given only in Figure III, which is not available, so the speed is left as $20\tau$. The original diagrams also left out what happens after the force stops: the acceleration drops to zero and the velocity stays constant.