The velocity-time ( v-t ) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t = 4 s is:

Step-by-step solution

From the given velocity-time graph, the particle is performing simple harmonic motion. The velocity starts from zero at t=0 and can be represented by a sine function: v(t) = v_ max ( t) From the graph, the maximum velocity is v_ max = 4 m/s and the time period is T = 8 s . The angular frequency is given by: = 2 T = 2 8 = 4 rad/s So, the equation for velocity as a function of time is: v(t) = 4 ( 4 t ) Acceleration a(t) is the rate of change of velocity: a(t) = dv dt = d dt [ 4 ( 4 t ) ] a(t) = 4 ( 4 ) ( 4 t ) = ( 4