Question

A car moving with initial velocity of $5$ mph accelerates at the rate of $a\left(t\right)=2.4t$ mph per second for $8$ seconds. Then answer the following question. How far did the car travel during those $8$ seconds?

• A. $0.68$ mile
• B. $0.068$ mile
• C. $0.60$ mile
• D. $0.060$ mile

Answer 1

The correct option is B $0.068$ mile

Velocity function=$1.2t^2+5$

Distance Travelled,

$\Rightarrow {\int }_0^8\left|v\left(t\right)\right|dt={\int }_0^8(1.2t^2+5)dt\Rightarrow {[1.2\frac{t^3}{3}+5t]}_0^8\Rightarrow {[0.4t^3+5t]}_0^8\Rightarrow 0.4{\left(8\right)}^3+5\left(8\right)-0.4(0{)}^3+5(0)\Rightarrow 244.8m/h\ast s\Rightarrow \frac{244.8miles\ast 1hr}{1hr\ast 3600s}$

$\Rightarrow 0.068$ mile is the correct answer