If
r→�→represents displacement vector and
v→=dr→dt�→=d�→d� represents the velocity, then;
Acceleration: a→=dv−→dt=d2v−→−d2t�→=d�→d�=d2�→d2�
In one dimensional motion, where x is the displacement, and
v=drdt�=d�d� is the Velocity, then;
a=dvdt=d2xd2t�=d�d�=d2�d2�
Example 1:
A car starts from rest and achieves a speed of 54
kmh��ℎ in 3 seconds. Find its Acceleration?
Solution:
v0�0 = 0,
vt�� = 54
kmh��ℎ = 15
ms��, t = 3s, a = ?
Acceleration:
a=vt−v0t=15−03=5ms2�=��−�0�=15−03=5��2
Example 2:
A body moves along the x- axis according to the relation
x=1–2t+3t2�=1–2�+3�2, where x is in meters and t is in seconds. Find the Acceleration of the body when t = 3 s
Solution:
We have:
x=1–2t+3t2�=1–2�+3�2
then; Velocity
v=dxdt=−2+6t�=d�d�=−2+6�
Acceleration:
v=dvdt=6ms2�=d�d�=6��2.
(We see that the Acceleration is constant here. Therefore, at t = 3s also, its value is 6
ms2��2).
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