Question

the acceleration time graph of a particle moving along a straight line as shown in fig .The time taken by particle to acquire it's initial velocity is
a 4s
b 8s
c 10s
d 5s​

Answer 1

Answer:

The particle acquires its velocity at 8 sec.

Explanation:

According to figure,

The velocity- time graph of a particle shows the change in velocity.

Let at time t₁ the particle acquire its initial velocity.

The change in velocity of particle in time t₁ is zero.

Area under the acceleration - time graph is zero

The area of Δ AOB = area of Δ BCD

\dfrac{1}{2}\times OA\times OB=\dfrac{1}{2}\times BC\times CD

2

1

×OA×OB=

2

1

×BC×CD

OB \tan\theta\times\ OB=CD\ tan\theta\times\ CDOBtanθ× OB=CD tanθ× CD

(OB)^2=(CD)^2(OB)

2

=(CD)

2

OB=CDOB=CD

4=t_{1}-44=t

1

−4

t_{1}=8\ sect

1

=8 sec

Hence, The particle acquires its velocity at 8 sec.