Question:
A horse rider covers half the distance with $5\, m / s$ speed The remaining part of the distance was travelled with speed $10\, m / s$ for half the time and with speed $15\, m / s$ for other half of the time The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7} m / s$ The value of $x$ is _____
A horse rider covers half the distance with $5\, m / s$ speed The remaining part of the distance was travelled with speed $10\, m / s$ for half the time and with speed $15\, m / s$ for other half of the time The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7} m / s$ The value of $x$ is _____
Updated On: Mar 19, 2025
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Correct Answer: 50
Solution and Explanation
The correct answer is 50.
tAB=\(\frac{x}{5m/s}\)
In motion BC
x=d1+d2
where d1&d2 we the distance travelled with 10 m/s and 15m/s respectively in equal time intervals
2t′ each
d1=\(\frac{10t}{2}\),d2=\(\frac{15t}{2}\)
d1+d2=x=\(\frac{t}{2}\)(10+15)=\(\frac{25t}{2}\)
v=\(\frac{2x}{\frac{x}{5}+\frac{2x}{25}}\)=750m/s
tAB=\(\frac{x}{5m/s}\)
In motion BC
x=d1+d2
where d1&d2 we the distance travelled with 10 m/s and 15m/s respectively in equal time intervals
2t′ each
d1=\(\frac{10t}{2}\),d2=\(\frac{15t}{2}\)
d1+d2=x=\(\frac{t}{2}\)(10+15)=\(\frac{25t}{2}\)
v=\(\frac{2x}{\frac{x}{5}+\frac{2x}{25}}\)=750m/s
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.