Question

A particle is moving according to the equation x = 4tsquare +5t, Find its
velocity and acceleration at time instant 2s
Your answer​

Answer 1

Explanation:

Given,

x=4t

2

+5t+16

y=5t

velocity along x-axis

v

x

=

dt

dx

=(8t+5)m/s

acceleration along x-axis,

a

x

=

dt

v

x

=8m/s

velocity alon y-axis

v

y

=

dt

dy

=5m/s

acceleration along y- axis,

a

y

=

dt

v

y

=0m/s

The acceleration of the particle is given by

a

=a

x

i

^

+a

y

j

^

∣

a

∣=

a

x

2

+a

y

2

a=

8

2

+0

2

=8m/s

2

The correct option is A.

Answer 2

Explanation:

$x = 4 {t}^{2} + 5t$

$v = \frac{dx}{dt} = \frac{d(4 {t}^{2} + 5t )}{dt} = 8t + 5$

velocity at t=2s

v = 8t + 5 = 8×2 + 5 = 16+5=21m/s

$a = \frac{dv}{dt} = \frac{d(8t + 5)}{dt} = 8$

acceleration (a) = 8 m/s^2