Question 45: Motion in 1D

Question

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 :

Accepted Answer

A small toy begins to move from a standstill with a constant acceleration. It covers a distance of 10 meters in t seconds. We need to determine the distance the toy will travel in the subsequent t seconds.
First, we know that the initial distance traveled is given by the formula for constant acceleration starting from rest:
$$\frac{1}{2} a t^2 = 10 	ext{ m}$$
Next, we calculate the total distance traveled after 2t seconds:
$$\frac{1}{2} a (2t)^2 = \frac{1}{2} a \cdot 4t^2 = 2 a t^2$$
Since we know from the initial condition that $ \frac{1}{2} a t^2 = 10 	ext{ m} $, multiplying it by 4 gives
$$2 a t^2 = 40 	ext{ m}$$
Thus, the additional distance traveled in the next t seconds is:
$$	ext{Total distance after 2t seconds} - 	ext{Distance already traveled in t seconds}$$
$$= 40 	ext{ m} - 10 	ext{ m}$$
$$= 30 	ext{ m}$$

Answer

10 m

Answer

20 m

Answer

30 m

Answer

40 m

Motion in 1D

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 :

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