A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by the toy in the next t s will be :

Solution

Physics sir · 3 steps

From rest, distances in equal time intervals go 1 : 3 : 5, so the next t s covers three times 10 m.

1. First t seconds. Starting from rest, s = 1/2at². So 1/2at² = 10 m.
2. After 2t seconds. The total distance in time 2t is 1/2a(2t)² = 4 × 1/2at² = 40 m.

   sₙₑₓₜ = s(2t) - s(t) = 40 - 10 = 30 m

3. So. The toy covers 30 m in the next t seconds, option (c). This matches Galileo's ratio 1 : 3 for the first two equal intervals.

The idea to keep. For motion from rest with constant acceleration, distances in successive equal time intervals are in the ratio 1 : 3 : 5 : 7, the odd numbers.

Answer from the NTA final answer key. Solution by PrepWiser.