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.

Question

A car starts from rest and accelerates uniformly at 3 m/s\textsuperscript{2. What will be its velocity after 5 seconds?}

Answer 1

Given:

Distance between home and office = 2.5 km
Speed while walking = 5 km h⁻¹
Speed while returning by auto = 25 km h⁻¹

Start time = 9:00 am
Stays at office till = 5:00 pm

Step 1: Calculate time taken to go to office

Time = Distance / Speed

Time taken = 2.5 / 5 = 0.5 h = 30 minutes

So, she reaches the office at:
9:30 am

Step 2: Calculate time taken to return home

Time taken = 2.5 / 25 = 0.1 h = 6 minutes

She starts from office at 5:00 pm and reaches home at:
5:06 pm

Step 3: Choose scales for the x–t graph

Let:

Take home as origin (x = 0).
Direction from home to office is taken as positive.

Step 4: Plotting the x–t graph

Plot the following key points on the graph:

Join:

Description of the x–t graph:

From 9:00 am to 9:30 am: Straight line with positive slope (uniform walking speed)
From 9:30 am to 5:00 pm: Horizontal line (position constant)
From 5:00 pm to 5:06 pm: Steep straight line downward (higher speed return)

Final Answer:

The x–t graph consists of three straight-line segments representing walking, rest, and fast return by auto, drawn using the chosen scales.

Solution and Explanation