Question

 The displacement of the particle is represented by s = 3t2 + 6t + 2. Where s is in meter and t is in second. Then for the particle.
1)graph of acceleration wrt to time is a straight line parallel to time axis.
2)
graph of acceleration wrt to time is a straight line of slope 6
3)graph of velocity wrt to time is parabola.
4)particle is moving with constant speed.​

Answer 1

answer : option (1) is correct.

The displacement of the particle is represented by S = 3t² + 6t + 2

differentiating with respect to time,

dS/dt = 6t + 6

we know, rate of change of displacement with respect to time is known as velocity.

so, v = dS/dt = 6t + 6

here v is directly proportional to t, hence, graph of v versus t will be straight line.

so, option (3) and (4) are not correct options .

now, v = 6t + 6

differentiating with respect to time,

dv/dt = 6

we know, rate of change of velocity with respect to time is known as acceleration.

so, a = dv/dt = 6

here it is clear that a is constant e.g., 6

hence, graph of acceleration with respect to time is a straight line parallel to time axis.

so, option (1) is correct choice.

Answer 2

Answer:

Explanation:

answer : option (1) is correct.

The displacement of the particle is represented by S = 3t² + 6t + 2

differentiating with respect to time,

dS/dt = 6t + 6

we know, rate of change of displacement with respect to time is known as velocity.

so, v = dS/dt = 6t + 6

here v is directly proportional to t, hence, graph of v versus t will be straight line.

so, option (3) and (4) are not correct options .

now, v = 6t + 6

differentiating with respect to time,

dv/dt = 6

we know, rate of change of velocity with respect to time is known as acceleration.

so, a = dv/dt = 6

here it is clear that a is constant e.g., 6

hence, graph of acceleration with respect to time is a straight line parallel to time axis.

so, option (1) is correct choice