Question

A body starts from rest with an acceleration a1. After 2 seconds another body starts from rest with an acceleration a2. If the travel equal distances in the 5 second after starting from rest a1:a2 =?

Answer 1

Answer:

Body A:

Acceleration = a1

Time = t

s=u t+\frac{1}{2} a 1 . t^{2}

s=\frac{1}{2} a 1 . t^{2}

Since, we need to find distance travelled in 5th second, we need find the difference between the distance travelled in 5 seconds and the distance travelled in 4 seconds.

Distance travelled in 5th second:

s=\frac{1}{2} a 1 .(5)^{2}-\frac{1}{2} a 1 .(4)^{2}

s=4.5(a 1)

Body B:

Acceleration = a2

Time = t – 2

s=u t+\frac{1}{2} a 2 \cdot(t-2)^{2}

s=\frac{1}{2} a 2 .(t-2)^{2}

Distance travelled in 5th second:

s=\frac{1}{2} a 2 .(5-2)^{2}-\frac{1}{2} a 2 \cdot(4-2)^{2}

s=\frac{9}{2} a 2-\frac{4}{2} a 2

s=\frac{5}{2}(a 2)

s=2.5(a 2)

The distance are equal,

4.5(a 1)=2.5(a 2)

\frac{a 1}{a 2}=\frac{2.5}{4.5}

\Rightarrow \frac{a 1}{a 2}=\frac{5}{9}

The ratio of a1 : a2 is 5 : 9