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Motion in a Straight Line — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line4 Marks
Question
When an object is in motion, its position changes with time. So, the quantity that describes how fast is the position changingm w.r.t. time and in what direction is given by average velocity. It is defined as the change in position or displacement $(\triangle\text{x})$ divided by the time interval $(\triangle\text{t})$ in which that displacement occur. However, the quantity used to describe the rate of motion over the actual path, is average speed. It defined as the total distance travelled by the object divided by the total time taken.
  1. A $250m$ long train is moving with a uniform velocity of $45\ kmh^{-1}.$ The time taken by the train to cross a bridge of length $750m$ is:
  1. $56s$
  2. $68s$
  3. $80s$
  4. $92s$
  1. A truck requires 3hr to complete a journey of $150\ km$. What is average speed?
  1. $50\ km/h$
  2. $25\ km/h$
  3. $15\ km/h$
  4. $10\ km/h$
  1. Average speed of a car between points $A$ and $B$ is $20\ m/s$, between $B$ and $C$ is 15m/s and between $C$ and $D$ is $10\ m/s.$ What is the average speed between $A$ and $D$, if the time taken in the mentioned sections is $20s, 10s$ and $5s,$ respectively?
  1. $17.14\ m/s$
  2. $15\ m/s$
  3. $10\ m/s$
  4. $45\ m/s$
  1. A cyclist is moving on a circular track of radius 40m completes half a revolution in $40s.$ Its average velocity is:
  1. $\text{Zero}$
  2. $2\text{ms}^{-1}$
  3. $4\pi\text{ms}^{-1}$
  4. $8\pi\text{ms}^{-1}$
  1. In the following graph, average velocity is geometrically represented by:
  1. Length of the line $P_1 P_2.$
  2. Slope of the straight line $P_1 P_2.$
  3. Slope of the tangent to the curve at $P_1.$
  4. Slope of the tangent to the curve at $P_2.$
✓

Answer

  1. (c) $80s$
Explanation:
Total time taken $=\frac{\text{Total distance}}{\text{Speed}}$
$\text{t}=\frac{250+750}{45\times\frac{5}{18}}=80\text{s}$
  1. (a) $50\ km/h$
Explanation:
Average speed $=\frac{\text{Total distance}}{\text{Total time}}$
$=\frac{150}{3}=50\text{km}/\text{h}$
  1. (a) $17.14\ m/s$ 
Explanation:
Total distance $(d = tv)$
$= 20 × 20 + 15 × 10 + 10 × 5 = 600\ m$
Total time $= 20 + 10 + 5 = 35\ s$
Therefore, average speed
$=\frac{600}{35}=17.14\text{m}/\text{s}$
  1. (b) $2\text{ms}^{-1}$
Explanation:
Given, $R = 40m $ and $t = 40s$
Average velocity $=\frac{\text{Total distance}}{\text{Time taken}}$
$=\frac{2\text{R}}{\text{t}}=\frac{2\times40}{40}=2\text{ms}^{-1}$
  1. (b) Slope of the straight line $P_1 P_2.$
Explanation:
From the position-time graph, average velocity is geometrically represented by the slope of curve, i.e. slope of straight line $P1 P2.$

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