Motion and integration question (1 Viewer)

[kqqq]

Hello!

I must be integrating incorrectly.

The acceleration of an object is given by a = e3t ms−2.
If initially the object is at the origin with velocity −2 ms−1, find its
displacement after 3 seconds, correct to 3 significant figures.

Answer= 893 m

I get the following as my velocity and displacement functions:

v= (e^3t)/3 -7

x= (e^3t)/6 -7t - 1/6

Thanks in advance!

 

[13cheungjn1]

Hi

Integrating exponentials: Divide by the derivative of the power

a = e^3t ms-2

v = 1/3 e^3t + C

When t = 0, v = -2
-2 = 1/3 e^0 + C
= 1/3 + C (as e^0 = 1)
C = -7/3

v = 1/3 e^3t -7/3

x = (1/3)/3 e^3t -7/3t + C
= (1/9) e^3t -7/3t + C

When t = 0, x = 0
0 = (1/9) e^(0) -7/3(0) + C
= 1/9 - 0 + C
C = -1/9

x = (1/9) e^3t -7/3t -1/9

Finding x when t = 3 gives you 893, hope that helps!

 

[kqqq]

Thanks so much!!!