A woman starts from her home at 9.00 am, walks with a speed of 5 km \(\text{h}^{-1}\)on a straight road up to her office 2.5 km away, stays at the office up to 5.00 pm, and returns home by an auto with a speed of 25 \(\text {km}\) \(\text{h}^{-1}\). Choose suitable scales and plot the x-t graph of her motion.
Solution and Explanation
Speed of the woman = 5 \(\text{km}/\text h\)
Distance between her office and home = 2.5 \(\text{km}\)
Time taken = \(\frac{\text{Distance}}{\text{Speed}}\)
= \(\frac{25.5}{5}\) = 0.5\(\text h\) = 30 \(\text {min}\)
It is given that she covers the same distance in the evening by an auto.
Now, speed of the auto = 25 \(\text{km}/\text h\)
Time taken = \(\frac{\text{Distance}}{\text{Speed}}\)
= \(\frac{2.5}{25}\) = \(\frac{1}{10}\) = 0.1 \(\text h\) = 6 \(\text {min}\)
The suitable x-t graph of the motion of the woman is shown in the given figure.
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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.