(25) Given figure shows a graph at acceleration — time for a rectilinear motion. Find average
acceleration in first 10 seconds.
-
10-
5
TO 15mm
(A) 1Oms
(B) 15ms
(C) 7.5ms
(D) 30ms 2
Answers
Answer:
First, let us make some simplifications in notation. Taking the initial time to be zero, as if time is measured with a stopwatch, is a great simplification. Since elapsed time is
Δ
t
=
t
f
−
t
0
, taking
t
0
=
0
means that
Δ
t
=
t
f
, the final time on the stopwatch. When initial time is taken to be zero, we use the subscript 0 to denote initial values of position and velocity. That is,
x
0
is the initial position and
v
0
is the initial velocity. We put no subscripts on the final values. That is, t is the final time, x is the final position, and v is the final velocity. This gives a simpler expression for elapsed time,
Δ
t
=
t
. It also simplifies the expression for x displacement, which is now
Δ
x
=
x
−
x
0
. Also, it simplifies the expression for change in velocity, which is now
Δ
v
=
v
−
v
0
. To summarize, using the simplified notation, with the initial time taken to be zero,
Δ
t
=
t
Δ
x
=
x
−
x
0
Δ
v
=
v
−
v
0
,
where the subscript 0 denotes an initial value and the absence of a subscript denotes a final value in whatever motion is under consideration.
–
a
=
a
=
constant
.