Question

The displacement S of a particle at time t is
given by S= t³- 4t² - 5t. Find the velocity and
the acceleration at t = 2.
(3 marks)​

Answer 1

Answer:

-9 L/T

4 L/T²

Step-by-step explanation:

The displacement s of a particle at a time t is given by s = t³ - 4t² - 5t. Find its velocity and acceleration at t = 2.

Velocity = d(Displacement)/dt  = ds/dt

ds/dt = d(t³ - 4t² - 5t)/dt

=> ds/dt =  3t² - 8t - 5

Velocity at t = 2

3(2)² -8(2) -5

= 12 - 16 -5

= -9 L/T

Acceleration = dv/dt

dv/dt  = d (3t² - 8t - 5)/dt

=> dv/dt  = 6t - 8

acceleartion at t = 2

6*2 - 8

= 4 L/T²

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Answer 2

$\texttt{The displacement S is given by}$

S

$= {t}^{3} - 4 {t}^{2} - 5t \\ \\ \\ v = \frac{dS}{dt} = 3 {t}^{2} - 4(2t) - 5(1) \\ \\ v = 3 {t}^{2} - 8t - 5$

$\frac{dS}{dt}_{t=2}=3 {2}^{2} - 8(2) - 5 \\ \\ = 12 - 16 - 5 \\ \\ = - 9 \\ \\ a = \frac{dv}{dt} = 3(2t) - 8(1) - 0 \\ \\ = 6t - 8$

$\frac{dv}{dt}_{t=2} = 6(2) - 8 \\ \\ = 12 - 8 \\ \\ = 4$

$\texttt{Velocity at t=2 is -9 and acceleration at t=2 is 4}$