Question

Q3. On mountainous downhill roads, escape routes are sometimes placed on the side of the road for trucks whose brakes might fail. Assuming a constant upward slope of 26, calculate the horizontal and vertical components of the acceleration of a truck that slowed from 110 kms to rest in 7.0 seconds.

Answer 1

We know the equation of motion,

..................................(1)

Where, is the final velocity of the object

u is the initial velocity of the object

a is acceleration of the object

t is time of motion

According to the question,

u = 110 km/s = 110 x 10³ m/s

= 0 m/s (as the truck finally stops)

t = 7.0 s

Putting these values in equation (1), we get

or,   

or,   

or,   

The negative sign is indicating that the acceleration is in opposite direction of velocity (i.e. in upward direction) .

The components of the acceleration are

Where,

and

Hence, the acceleration in component form can be written as

Hence, the horizontal component of acceleration is 14.11 km/s² in negative - x direction and the vertical component of acceleration is 6.882 km/s² in y - direction (i.e. in upward direction).

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