A car moves a distance of 200 m. It covers first half of the distance at speed 60 kmh–¹ and the second half at speed v. If the average speed is 40 kmh–¹, the value of v is
\[ V_{av}= \frac{2V_{1}.V_{2}}{V_{1}+V_{2}}\]
\[ 40= \frac{2\times 60\times V_{2}}{ 60+V_{2}} \]
\[ V_{2}= 30 m/s \]
A body of mass m moving along a straight line covers half the distance with a speed of 2 ms–¹. The remaining half of distance is covered in two equal time intervals with a speed of 3 ms–¹ and 5 ms–¹ respectively. The average speed of the particle for the entire journey is
For Second Half of Journey
\[ V_{av}=\frac{3+5}{2}= 4 m/s \]
\[ V_{av}= \frac{2\times 2 \times 4}{2+4}= \frac{8}{6}= \frac{4}{3} \]
Velocity-time graph of a particle is given as :
then average speed of particle from t = 0 to t = 5 sec is :
Area bounded with Velocity time graph represents displacement. Magnitude of Area bounded by Velocity time graph represents distance.
Total Area = 60 so, distance = 60 m and time = 5 sec.
Average speed = 12 m/s
A car is moving along a straight line OP as shown in the figure. It moves from O to P in 18 s and returns from P to Q in 6 s. Which of the following statements is not correct regarding the motion of the car :
Total Distance = OP + PQ = 360 + 120 = 480 m
Displacement = OQ= 240 m
Average Speed = 480/24 = 20 m/s
Average Velocity= 240/24= 10 m/s
A scooter is going towards east at 10 ms–¹ turns right through an angle of 90°. If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is :
Change in a vector when it is rotated by an angle θ is
\[ \Delta V = 2V sin \left( \frac{\theta}{2} \right) \]
\[ \Delta V = 2\times 10 sin \left( \frac{90^{0}}{2} \right)= 20/\sqrt{2}= 10\sqrt{2}= 14.4 m/s \]
Figure shows position versus time graph of two rabbits running opposite to each other between two trees. Which of the following statements are true.
Distance is equal for both A and B. B is taking lesser time to complete so its speed is higher.