Question

A body which is uniformly retarded comes to rest at 10 seconds after travelling a distance of 20 meters. calculate the initial velocity

Answer 1

To calculate the initial velocity of a body that is uniformly retarded, we can use the equations of motion. Given the following information:

- Distance traveled (s) = 20 meters
- Time taken (t) = 10 seconds
- Final velocity (v) = 0 m/s (as it comes to rest)

We can use the second equation of motion:

\[
s = ut + \frac{1}{2} a t^2
\]

Where:
- \( s \) is the distance,
- \( u \) is the initial velocity,
- \( a \) is the acceleration (deceleration in this case),
- \( t \) is the time.

We can also relate \( u \), \( v \), and \( a \) using the first equation of motion:

\[
v = u + at
\]

Since the body comes to rest, \( v = 0 \). Thus:

\[
0 = u + at
\]

From this, we can express acceleration \( a \):

\[
a = -\frac{u}{t}
\]

Now, substituting \( a \) back into the second equation of motion:

\[
s = ut + \frac{1}{2} \left(-\frac{u}{t}\right) t^2
\]
\[
s = ut - \frac{1}{2} ut
\]
\[
s = ut \left(1 - \frac{1}{2}\right)
\]
\[
s = \frac{1}{2} ut
\]

Now we can solve for \( u \):

\[
u = \frac{2s}{t}
\]

Substituting the values of \( s \) and \( t \):

\[
u = \frac{2 \times 20 \text{ m}}{10 \text{ s}} = \frac{40 \text{ m}}{10 \text{ s}} = 4 \text{ m/s}
\]

Thus, the initial velocity \( u \) is \( \mathbf{4 \ m/s} \).