A car travels in a straight line along a road | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The average velocity $v_{avg}$ is defined as the total change in displacement divided by the total time interval: $v_{avg} = \frac{\Delta x}{\Delt

Vedclass · Accepted Answer

$2.28$

Vedclass · Answer

(A) The average velocity $v_{avg}$ is defined as the total change in displacement divided by the total time interval: $v_{avg} = \frac{\Delta x}{\Delta t} = \frac{x(t_2) - x(t_1)}{t_2 - t_1}$.Given $x(t) = \alpha t + \beta t^3$ with $\alpha = 2.0 \ m \ s^{-1}$ and $\beta = 0.01 \ m \ s^{-3}$.At $t_1 = 2.00 \ s$: $x(2) = 2.0(2) + 0.01(2)^3 = 4.0 + 0.01(8) = 4.08 \ m$.At $t_2 = 4.00 \ s$: $x(4) = 2.0(4) + 0.01(4)^3 = 8.0 + 0.01(64) = 8.64 \ m$.Now, calculate the average velocity: $v_{avg} = \frac{8.64 - 4.08}{4.00 - 2.00} = \frac{4.56}{2} = 2.28 \ m \ s^{-1}$.

Similar Questions

$A$ particle moves along a semicircle of radius $10\,m$ in $5$ seconds. The average velocity of the particle is...........$m/s$.

$A$ person walks along a straight road from his house to a market $2.5 \,km$ away with a speed of $5 \,km/h$ and instantly turns back and reaches his house with a speed of $7.5 \,km/h$. The average speed of the person during the time interval $0$ to $50 \,min$ is (in $m/s$)

Give the difference between average speed and average velocity.

$A$ person travelling on a straight line moves with a uniform velocity $v_1$ for a distance $x$ and with a uniform velocity $v_2$ for the next $\frac{3}{2} x$ distance. The average velocity in this motion is $\frac{50}{7} \ m/s$. If $v_1$ is $5 \ m/s$,then $v_2 = $ . . . . . . $m/s$.

$A$ car moving on a straight road covers one-third of the distance with $20 \, km/hr$ and the rest with $60 \, km/hr$. The average speed is .......... $km/hr$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module