Question

A particle moves along +x-axis with initial velocity 5 m/s. If acceleration (a) varies with time (t) as shown in a-t graph, then the velocity of the particle just after 4 second is

• A. $2.5m/s$
• B. $10m/s$
• C. $-1.25m/s$
• D. $-5m/s$

Answer 1

Answer: (C)

$-1.25m/s$

Area under the $a-t$ graph gives the change in the velocity because $dv=adt$

so the change in velocity i.e area is $\Delta v=\text{positive rectangle + positive triangle + negative big triangle}$

or $\Delta v=5\times 1+\frac{1}{2}\times (1.5-1)\times 5-\frac{1}{2}\times (4-1.5)\times 10=-6.25m/s$

so the new velocity will be $v_i+\Delta v=5-6.25=-1.25m/s$