Question

A body has an initial velocity of 25 m/s in the negative x-direction. The following figure represents it's a - t graph. Find its displacement at t = 15s.

• A. 0 m
• B. 50 m
• C. 125 m
• D. 250m

Answer 1

The correct option is C

125 m

t = 0 to t = 5s

u = -25 m/s, a = 10 m/$s^2$ , t = 5s

v = u + at

= -25 + (10)(5)

= -25 + 50

= 25 m/s $\therefore$ Velocity at 5s = 25 m/s

s = ut + $\frac{1}{2}a{t}^2$

= -25(5) + $\frac{1}{2}\left(10\right)(5{)}^2$

= -125 + 125

= 0 $\therefore$ net displacement = 0

From t = 5 to t = 5

u = 25 m/s, a = 0, t = 5

$\therefore$ s = 25 $\times$ 5 = 1125 m

From t = 10 to t = 15

u = 25 m/s, a = -10 m/s, t = 5

s = ut + $\frac{1}{2}a{t}^2$

= 25(5) + $\frac{1}{2}(-10)\left(5\right)2$

= 125 - 125 = 0

$\therefore$ Net displacement = 0 + 125 + 0 = 125m

$\underset{–}{Graphicalsolution}$

From the graph, area under the graph will give displacement.

$\therefore$ Area under the graph =

-ar $△$OAB + ar$△$CAE + ar$△$CEFD + ar$△$ADFG - ar$△$GIH

AsOA = AE = FG = GI ( by AA symmetry)

ar$△$OAB = ar$△$CAE

ar $△$DFG = ar $△$GIH

$\therefore$ Area under the graph

= area oCEFD

= 25 × 5

= 125 m