Test: Translational Motion and Calculations - 2 - MCAT MCQ

To find displacement with constant acceleration, we can use the formula: d= Δt (v_a)

Our Δt should simply be the time it takes to go from 15 m/s to 30 m/s at an acceleration of 5 m/s²: Δv = aΔt or 15 =  5Δt, which gives us Δt = 3.

Our v_a is simply the average velocity, which we can calculate using: v_a = 1/2(v_f + v_i) or va = 1/2 (30+15) which gives us v_a = 22.5 m/s

Using our initial formula, d = Δt (v_a), d = 3 sec x 22.5 m/s or d = 67.5m

To find displacement on a velocity vs. time graph, we simply can calculate the area under the curve.

To calculate the area, we can split the graph into geometric shapes by drawing vertical lines at times 3, 5, and 9. This gives us 4 right triangles and one rectangle.

The two larger triangles have equal areas of ½ (2x2) which those two combined gives us an area of 4. The rectangle has an area (2x2) giving us an area of 4. Finally the last two smaller triangles have an area of ½ (1x1) giving us a combined area of 1.

Adding up these areas then, we have 4+4+1, or 9m total.

We can relate time and displacement with constant deceleration just the same as we can with constant acceleration, with the formula d= Δt (v_a).

We know displacement must equal 2,000m, therefore we can plug in our values to solve for Δt.

2000 = Δt 1/2(0+72), therefore Δt = 55.55 or roughly 56 seconds.

To find displacement with constant acceleration, we can use the formula: d = Δt (v_a)

Our Δt should simply be 11 secs

Our v_a​ is simply the average velocity, which we can calculate using: v_a = 1/2(v_f + v_i) or v_a = ½ (0+60) which gives us v_a = 30 m/s

Using our initial formula, d = Δt (v_a), d = 11 sec x 30 m/s or d = 330 m

Remember that acceleration is the measure of a change in velocity [(m/s)/s] over time, while velocity is the change of displacement over time. (m/s)

Since this graph is of displacement over time, it only measures velocity.

Since the velocity (slope) is constant from minute 6 to minute 8, that means there is no change in velocity, meaning there is no acceleration. If the object has no acceleration, then the acceleration is 0.

The vector quantity representing magnitude and direction is velocity, not speed

Because speed is not a vector quantity, constant speed cannot tell us direction of an object. Therefore you can move at constant speed but still accelerate by changing direction.

Displacement of an object could equal zero simply by moving in a circle. If your initial and final positions are the same, your displacement is zero but your speed is not.

An object can only experience an increase in speed if it is accelerated.

We are given displacement and time, and we also know our initial velocity is 0, therefore we can use the formula: d = 1/2at² 

We can plug in our values and solve for acceleration. 400m = ½ a 4² 

One trick to avoid having to calculate 800/16 mentally is to first divide both sides of the equation by 4, to simplify the equation to: 100m = ½ 4a. This of course gives us a = 50 m/s².

We are give velocity and time, and must find average acceleration, therefore we can use the equation a = v/t

Remember upon plugging in our values we have to make sure we use the correct units, in this case we are expected to solve for meters/sec, which we would want to convert from km/hr.

1223.65 km/hr x (1hr / 3600 sec) x (1000 m / 1 km) = 339.9 m/s

We must then take the value in meters per second and plug it into our formula:
a = 339.9 m/s / 60 seconds
a = 5.67 m/s²

We are given time, as well as initial and final velocity. We can therefore use the formula: v = v₀ + at.

Convert minutes to seconds and plug in our values, we then get 8000 = 0 + 510 (a)

To do the math quickly without a calculator, remember that if a = 8 m/s² then our t would have to equal 1,000 seconds to reach 8,000 m/s. Therefore if our time is roughly half 1,000 seconds, then our acceleration should be roughly double 8 m/s² or 15 m/s²

We are given a final an initial velocity, as well as displacement, and we are looking for time. Since we have constant velocity, we can use the formula: d = vt.

Be careful plugging in our values! We have to convert km/hr into m/s for our formula to work.
169 km/hr x (1hr / 3600 sec) x (1000 m / 1 km)
This should give us a velocity of ~47 m/s.

Using our converted velocity, we can plug in our values:
18 = 47t
t = ~0.4 seconds