Question

Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the interval between 4th and 5th seconds.

July 25, 2024

Answer

Using the equation of motion s = $ut + {1 \over2}at^2$

Distance travelled in 5 seconds, s = $u \times 5 + {1\over2}a \times 5^2$

Or s = $5u+{25\over2}a$ …….(1)

Similarly, distance travelled in 4 seconds, s’ = $4u+{16\over2}a$ ….(2)

Distance travelled in the interval between 4^th and 5^th seconds

= (s – s’) = $(u+{9\over2}a)m$

💡 Some Related Questions

The table given below shows distance (n cm) travelled by bodies A, B and C. Read this data carefully and answer the following questions. Distance (in cm) covered by different bodies.

Time in (s) Body (A) Body (B) Body (C)

1stSecond 20 20 20

2ndSecond 20 36 60

3rdSecond 20 24 100

4thSecond 20 30 140

5thSecond 20 48 180

(i) Which of the bodies is moving with (a) constant speed? (b) constant acceleration? (c) non-uniform acceleration? (ii) Which of the bodies covers (a) maximum distance in 3rd second? (b) minimum distance in 3rd second?

Suppose a squirrel is moving at a steady speed from the base of a tree towards some nuts. It then stays in the same position for a while, eating the nuts, before returning to the tree at the same speed. A graph can be plotted with distance on the x-axis and the time on y-axis.

Observe the graph carefully and answer the following questions. (i) Which part of the graph shows the squirrel moving away from the tree? (ii) Name the point on the graph which is 6 m away from the base of the tree. (ii) Which part of the graph shows that the squirrel is not moving? (iv) Which part of the graph shows that the squirrel is returning to the tree? (v) Calculate the speed of the squirrel from the graph during its journey.

A girl walks along a straight path to drop a letter in the letterbox and comes back to her initial position. Her displacement-time graph is shown in figure. Plot a velocity-time graph for the same.

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with the help of a graph, derive the relation v = u + at.

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What are the characteristics of distance-time graph for an object moving with a non-uniform speed?