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Mechanics Question of objects on planes.

Voltozonic

(edited 10 years ago)

is this M3?

The question was solved using an assumption:
1. The car was at rest at the bottom of the hill.

Since the car is moving uphill, a component of gravity will be acting it, in downwards direction. Let this be g' (where g' = g sin 15).

Now, using s = ut + (1/2) a t², where the symbols have their usual meaning,
distance travelled in 30 sec :

s = (1/2)(a-g')(30²) = 450 (a-g').

after switching off the engine, the car comes to rest at some point. now, v = 0.

use v² - u² = 2 a s.
note that:
v=0
u = (a-g')(30) (using v=u+at)
a= (-g') (since it is in opposite direction of initial motion).

so, distance travelled after switching off the engine:
s' = [ { 30(a-g') }² ] / (2 g')

s' = 450 ( (a²)/g' - 2a + g' )

so, the 2 distances measured can be equal only if (a²)/g' - 2a + g' = (a²)/g'

so, 2a - g'= 0.

therefore, a = (1/2) g sin 15.

now, taking g= 9.8 and sin 15 = 0.25,

a = 1.225.

but a is given as 2.5, which means g'-2a is negative, so the car moved more in the first 30 seconds than for the rest of it's journey upwards.

Hope this helps. :smile: