Question

A particle moves along a straight line and its velocity depends on time at $V=4t-t^2$. Then for first 5 S

• A. average velocity is $\frac{25}{3}m/s$
• B. average speed is $\frac{5}{3}m/s$
• C. average velocity is $\frac{5}{3}m/s$
• D. acceleration is $-6\frac{m}{s^2}$

Answer 1

Answer: (C), (D)

The correct options are
C average velocity is $\frac{5}{3}m/s$
D acceleration is $-6\frac{m}{s^2}$

$\hat{V}=\frac{{\int }_0^{5}Vdt}{{\int }_0^{5}dt}=\frac{5}{3}m/sV=\frac{\left|{\int }_0^{4}Vdt\right|+\left|{\int }_4^{5}Vdt\right|}{{\int }_0^{5}dt}=\frac{13}{5}m/s$
$a=\frac{dV}{dT}=4-2t$