Question

The position of a ball is given by x(t) (2.3 m/s) .t + (5.3m/s3) t3. What is the position 348 m at time t 4 s? You are correct Your receipt no. is 163-61590 Part B What is the instantaneous velocity at t-4 s? Submit Answer Incorrect. Tries 2/6 Previous Tries Part C What is the instantaneous acceleration at time t4 s?

Answer 1

Answer:

(a) 348.4 m

(b) 256.7 m/s

(c)  127.2 m/s^2

Explanation:

$x = 2.3 t + 5.3 t^{3}$

(a) at t = 4 s

x = 2.3 x 4 + 5.3 x 4 x 4 x 4

x = 348.4 m

(b) The derivative of displacement function gives the value of instantaneous velocity.

So, v = dx / dt = 2.3 + 5.3 x 3 x t^2

v = 2.3 + 15.9 t^2

Put t = 4 s

So, v = 2.3 + 15.9 x 4 x 4

v = 256.7 m/s

(c) The derivative of velocity function with respect to time gives the value of instantaneous acceleration.

So, a = dv / dt = 5.3 x 3 x 2 x t

a = 31.8 t

Put t = 4 s

a = 31.8 x 4 = 127.2 m/s^2