Show that this equation is dimensionally correct. Average speed of travelling ca

Question

Show that this equation is dimensionally correct. Average speed of travelling car

1a) What is the average speed for the trip and the distance travelled between the cities?

A person makes a trip by a car between two cities. A record of the trip follows: 30.0 min at 80.0 km/h, 12.0 min at 1.00 x 10^2 km/h, 45.0 min at 40.0 km/h, and 15.0 min for lunch break and gas-up. Show that the equation V^2= v^2+ 2ax is dimensionally correct, where v and v0 represent velocities, a is acceleration, and x is a distance.

Explanation / Answer

a) Total distance travelled =

(30/60) * 80 + (12/60) * 100 + (45/60) * 40

= 40 + 20 + 30 = 90 kms

Total time taken = 30 + 12 + 45 + 15 = 102 minutes = 102/60 hrs

Average speed = total distance travelled / total time taken = 90 km / (102/60) hrs = 52.94 km/hr

b) The equation is v2 = v02 + 2ax

Consider Left hand side

The unit of v2 is (m/s)2 = m2/s2

Consider Right Hand Side :

v02 is also the square of velocity so its unit is again m2/s2

For 2ax, the unit is = (m/s2) * (m) = m2/s2

Hence unit on Left Hand Side = unit on Right Hand Side.

Hence, the eqaution is dimensionally correct.

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