Question

A particle starts from rest, accelerates at $2m{s}^{-2}$ for $10s$ and then goes for constant speed for $30s$ and then deceleration at $4m{s}^{-2}$ till stops after next. What is the distance travelled by it?

• A. $750m$
• B. $800m$
• C. $700m$
• D. $850m$

Answer 1

The correct option is A $750m$

Displacement in first, $10\sec$

$s_1=\frac{1}{2}{a}_1{t_1}^2=\frac{1}{2}\times 2\times {10}^2=100m$

Speed achieve in first $10\sec$

$v_1=u_1+a_1{t}_1=0+2\times 10=20m/s$

Displacement in $30\sec$, acceleration is zero.

$s_2=v_1{t}_2=20\times 30=600m$

Displacement in last due to deacceleration, $a_3=-4m/s^2$

$v^2-{v_1}^2=2as$

$s_3=\frac{0-{20}^2}{2\times (-4)}=50m$

Net displacement

$S_{total}=s_1+s_2+s_3=100+600+50=750m$

Total displacement is $750m$