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The acceleration-time graph of a particl...

The acceleration-time graph of a particle moving along x-axis is shown in the figure. If the particle starts with velocity 3 m/s at t = 0, find the velocity of particle at t = 4 s.

Text Solution

Verified by Experts

The velocity at t = 4 s will depend on the change in velocity of the particle in the interval 0 to 4 s which is given by the area under a-t graph. Before calculating area let us find the acceleration at t = 4 s.
`tantheta=(8-a_(0))/(4)=(8)/(8)" (by the graph)"`
`rArr" "a_(0)=4m//s^(2)`
`"Change in velocity "="Area between 0 to 4 s"`
`=(1)/(2)xx(4+8)xx4=24m//s`
`rArr" final velocity (v)"-"initial velocity (u) = 24"`
`rArr" "v=u+24=3+24=27m//s`
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Knowledge Check

  • The acceleration - time graph for a particle moving along x - axis is shown in figure, If the initial velocity of particle is -5m//s , the velocity at t = 8 s is

    A
    `+15m//s`
    B
    `+20m//s`
    C
    `-15m//s`
    D
    `-20m//s`

  • The acceleration time graph of a particle is shown in the figure-1.140. What is the velocity of particle at t=8s, if initial velocity of particle is 3 m/s? (Assume motion is 1 dimension) :

    A
    4 m/s
    B
    5 m/s
    C
    6 m/s
    D
    7 m/s

  • The acceleration-time graph of a particle moving in a straight line is as shown in figure. The velocity of the particle at time t = 0 is 2 m//s . The velocity after 2 seconds will be

    A
    `6 m//s`
    B
    `4 m//s`
    C
    `2 m//s`
    D
    `8 m//s`