Uniformly Accelerated Motion

Question

A car starting from rest accelerates uniformly at 2.5 m/s^2 along a straight road. What velocity will the car attain after 8 seconds of this acceleration?

RankGuru · Accepted Answer

For motion under constant acceleration the first equation of motion, $v = u + at$, relates the final velocity to the initial velocity, the acceleration, and the elapsed time. This equation follows directly from the definition of acceleration as the constant rate of change of velocity, integrated over the interval of motion. Here the car starts from rest, so the initial velocity $u = 0$. Substituting $a = 2.5	ext{ m/s}^2$ and $t = 8	ext{ s}$ gives $v = 0 + 2.5 	imes 8 = 20	ext{ m/s}$. The option 10 m/s is wrong because it corresponds to only 4 s of acceleration. The option 16 m/s incorrectly uses an acceleration of 2 m/s^2. The option 5 m/s confuses acceleration with velocity by reporting $a 	imes 2$. This is the standard NCERT kinematic relation for straight-line motion with uniform acceleration. As a unit check, multiplying m/s^2 by s correctly yields m/s, and the magnitude is physically reasonable for a car reaching about 72 km/h after eight seconds of brisk acceleration.

Uniformly Accelerated Motion

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