Answer to Question #91705 in Classical Mechanics for Louie

Question

The position of a particle which is constrained to move along a straight line is given by
x = 3t3 − 7t + 9 , where x is the position measured in metres from an origin and t is in seconds. Determine the acceleration of the particle when its velocity is 26 m/s.

Answer 1

Position of particle is given by function

$X=3t^3-7t+9$

D.w.t of position function gives velocity function

$V=\frac{dX}{dt}=9t^2-7$ ------------------------(1)

But Velocity is given as V=26 m/s

$26=9t^2-7$

t²=33/9

t=1.91sec

Now differentiate again the velocity function equation (1) with respect to t, we get acceleration function

$A=\frac{dV}{dt}=18t$

A=18x1.91

A=34.38m/s²