Question

An object starts from rest and accelerate uniformly down an incline. If the object reach with speed of 40m/s in 5 seconds, its average speed is a) m/s (b) 10m/s (c) 20m/s (d) 30m/s​

Answer 1

Answer:

Explanation:

Since v = u + at

Here u = 0 v = 40 nd t = 5

Hence a = 8m/s²

Now total distance covered in 5 second = 1/2 at²

= 1/2 X 8 X 25 = 100m

Nd hence average speed = 100/5 = 20m

Answer 2

Given:

Initial velocity $u=0m/s$

Final velocity $v=40m/s$

Time $t=5s$

To find:

Average speed of the object $(V_{avg} )$

Solution:

Step 1

We have been given that an object initially at rest slides down an incline plane and reaches with a final velocity 40 m/s in 5 s.

The acceleration with which the body slides down the inclined plane is given by

$v=u+at$  

We have,  $u=0m/s$   ;  $v=40m/s$    ; $t=5s$

We get

$40=0+a(5)$

$a=8m/s^{2}$

Hence, the object slides down the inclined plane with an acceleration of 8 m/s².

Step 2

Now, length of the inclined plane is given by

$v^{2}- u^{2}=2as$

We have,  $u=0m/s$   ; $v=40m/s$   ; $a=8m/s^{2}$

We get

$(40)^{2}- (0)^{2}=2(8)s$

$s=100m$

Step 3

Now,

We know, average speed of an object is the total distance traveled by the object throughout the journey upon the total time taken by the object.

$V_{avg}=\frac{total-distance-traveled}{total-time-taken}$

We have,

Total distance $s=100m$

Total time taken $t=5s$

We get

$V_{avg}=\frac{100}{5}$

$V_{avg}=20m/s$

Final answer:

Hence, the average speed of the object through the journey is 20 m/s.