Question

Acceleration time graph of a car moving on level ground is given. If the car starts from rest, then distance travelled by it in 6 sec is

• A. 80 m
• B. 48 m
• C. 50.66 m
• D. 46.8 m

Answer 1

The correct option is C 50.66 m

$a=2t\text{for}0\le t\le 2\Rightarrow {\int }_0^{v}dv={\int }_0^{t}2tdtv=\frac{2}{2}(t^2{)}_0^t\Rightarrow v=t^2\Rightarrow {\int }_0^{x_1}dx={\int }_0^2{t}^{2}dt{x}_1={\int }_0^{t}vdt=\frac{{\left(t^3\right)}_0^2}{3}=\frac{8}{3}=2.66\Rightarrow x_2=ut+\frac{1}{2}a{t}^2{x}_2=4\times 4+\frac{1}{2}\times 4\times 4^2=16+32=48x=x_1+x_2=50.66m$