equations of motion

Question

A car accelerates uniformly from rest to a velocity of 25 m/s in 5 seconds. What is the distance covered during this time?

RankGuru · Accepted Answer

1. **Identify Given Data**:
   - Initial velocity $u = 0$ (from rest).
   - Final velocity $v = 25$ m/s.
   - Time $t = 5$ s.
2. **Find Acceleration ($a$)**: Using $v = u + at$
   - $25 = 0 + a(5) \implies a = 5$ m/s$^2$.
3. **Calculate Distance ($s$)**: Using $s = ut + \frac{1}{2}at^2$
   - $s = 0(5) + \frac{1}{2}(5)(5)^2$
   - $s = 2.5 	imes 25 = 62.5$ m.
4. **Alternative Method**: Using average velocity for constant acceleration:
   - $s = \left( \frac{u+v}{2} ight) t = \left( \frac{0+25}{2} ight) 	imes 5 = 12.5 	imes 5 = 62.5$ m.

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