Question

find the acceleration uniform a body, initially at rest, starts moving with a constant acceleration 2 m s⁻². calculate : (i) the velocity acquired and (ii) the distance travelled in 5 s. a bullet initially moving with a velocity 20 m s⁻¹ strikes a target and comes to rest after penetrating a

Explanation:

Part (i): Velocity Acquired

Step1: Identify known values

Initial velocity \( u = 0 \, \text{m/s} \) (at rest), acceleration \( a = 2 \, \text{m/s}^2 \), time \( t = 5 \, \text{s} \).
We use the first equation of motion: \( v = u + at \).

Step2: Substitute values into formula

Substitute \( u = 0 \), \( a = 2 \), \( t = 5 \) into \( v = u + at \):
\( v = 0 + (2)(5) \)

Step3: Calculate velocity

\( v = 10 \, \text{m/s} \)

Part (ii): Distance Travelled

Step1: Identify known values

Initial velocity \( u = 0 \, \text{m/s} \), acceleration \( a = 2 \, \text{m/s}^2 \), time \( t = 5 \, \text{s} \).
We use the second equation of motion: \( s = ut + \frac{1}{2}at^2 \).

Step2: Substitute values into formula

Substitute \( u = 0 \), \( a = 2 \), \( t = 5 \) into \( s = ut + \frac{1}{2}at^2 \):
\( s = (0)(5) + \frac{1}{2}(2)(5)^2 \)

Step3: Simplify and calculate

Simplify: \( s = 0 + \frac{1}{2}(2)(25) = 25 \, \text{m} \)

Answer:

s:
(i) The velocity acquired is \( \boldsymbol{10 \, \text{m/s}} \).
(ii) The distance travelled in \( 5 \, \text{s} \) is \( \boldsymbol{25 \, \text{m}} \).