Question

If motion of a particle is given by S=t^3+t^2-t+2 find it's position, velocity and acceleration of the particle after 2seconds
Answer quickly

Answer 1

here concept used is differentiation , if u are unknown of this concept u can used another method too bt this is the easiest one.

Answer 2

Concept:

• Differentiation
• Displacement, velocity and acceleration

Given:

• displacement s = t³+t²-t+2
• time t = 2 s

Find:

• the position after 2 s
• the velocity after 2 s
• the acceleration after 2 s

Solution:

Position

s = t³+t²-t+2

t = 2

s =  2³+2²-2+2

s = 8 + 4 = 12

s = 12 m

v = ds/dt

v = d(t³+t²-t+2)/dt

v = 3t² + 2t - 1

t = 2

v = 3 (2)² + 2(2) - 1

v = 3(4) + 4-1

v = 12 + 3

v = 15 m/s

a = dv/dt

a = d (3t² + 2t - 1)/ dt

a = 6t + 2

t = 2

a = 6(2) +2

a = 12+2 = 14

a = 14 m/s²

The position is 12 m, the velocity is 15 m/s and the acceleration of the particle is 14 m/s².

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