A body moves along a straight line with a uniform acceleration. The distance covered by the body in time t is given by what?
Answers
Answer:
ANSWER
The distance covered in n
th
second,
S
n
=u+
2
a
(2n−1) . . . . . . . . . . .(1)
For n=3 and S
3
S
3
=u+
2
a
(6−1)=10
10=u+
2
5a
. . . . . . . . .(2)
For n=4 and S
4
=12m
S
4
=u+
2
a
(8−1)
12=u+
2
7a
. . . . . . . . .(3)
Subtract equation (3) by equation (2),
12−10=(u+
2
7a
)−(u+
2
5a
)
a=2m/s
2
From equation (2),
10=u+
2
5×2
10=u+5
u=5m/s
Answer:
s=ut+1/2at² is the distance covered by the body in time t.
DERIVATION:
Consider an object which has travelled displacement s in the time t under uniform acceleration a.Let intial velocity of the object be u and the final velocity v.
s=1/2t(u+v)------1
from the veocity relation
v=u+at-------------2
substitute 1 in 2
s=1/2t (u + u + at)
=1/2t (2u + at)
s=ut+1/2at².
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