Kutumas - Equations of motion. To find or calculate the acceleration of an moving object, we can use the equations of motion. Equations of motion shows the relation between velocity, time, displacement, and acceleration. There are three equations of motion we can use to calculate te acceleration.
Note :
vi = initial velocity (m/s)
vf = final velocity (m/s)
a = acceleration (m/s2)
t = time (s)
Δx = displacement (m).
Example :
A racing car is travelling north. It accelerates uniformly covering a distance of 500 m in 10 s. If the initial velocity of it is 10 m/s, the acceleration is ....
A. 6 m/s2 north
B. 8 m/s2 north
C. 10 m/s2 north
D. 12 m/s2 north
E. 16 m/s2 north
Answer :
Step 1 : Identify the information given
To identify what information is given, we must read the questions well. One of the best way to find them is by concern on the units. From the question above, we are given :
1). vi = 10 m/s
2). Δx = 500 m
3). t = 10 s
Step 2 : Identify what is asked for
The question above asks us to find the acceleration of the racing car, so:
⇒ a = .... ?
Step 3 : Find the relating equations
Next, find an equation of motion relating the given information to the acceleration. We can use one of three equations above. For solve this problem, we can use the third equation.
⇒ Δx = vi.t + ½ a.t2
Step 4 : Substitute the value in and calculate the answer
We have vi = 10 m/s, Δx = 500 m, and t = 10 s, so :
⇒ Δx = vi.t + ½ a.t2
⇒ 500 = 10 (10) + ½ a. (10)2
⇒ 500 = 100 + ½ a (100)
⇒ 500 = 100+ 50 a
⇒ 500 - 100 = 50a
⇒ 400 = 50a
⇒ a = 400/50
⇒ a = 8 m/s2
Step 5: Quote the final answer
Based on the calculation above, the racing car is accelerating at 8 m/s2 north.
| vf = vi + a.t |
| vf2 = vi2 + 2a.Δx |
| Δx = vi.t + ½ a.t2 |
Note :
vi = initial velocity (m/s)
vf = final velocity (m/s)
a = acceleration (m/s2)
t = time (s)
Δx = displacement (m).
Example :
A racing car is travelling north. It accelerates uniformly covering a distance of 500 m in 10 s. If the initial velocity of it is 10 m/s, the acceleration is ....
A. 6 m/s2 north
B. 8 m/s2 north
C. 10 m/s2 north
D. 12 m/s2 north
E. 16 m/s2 north
Answer :
Step 1 : Identify the information given
To identify what information is given, we must read the questions well. One of the best way to find them is by concern on the units. From the question above, we are given :
1). vi = 10 m/s
2). Δx = 500 m
3). t = 10 s
Step 2 : Identify what is asked for
The question above asks us to find the acceleration of the racing car, so:
⇒ a = .... ?
Step 3 : Find the relating equations
Next, find an equation of motion relating the given information to the acceleration. We can use one of three equations above. For solve this problem, we can use the third equation.
⇒ Δx = vi.t + ½ a.t2
Step 4 : Substitute the value in and calculate the answer
We have vi = 10 m/s, Δx = 500 m, and t = 10 s, so :
⇒ Δx = vi.t + ½ a.t2
⇒ 500 = 10 (10) + ½ a. (10)2
⇒ 500 = 100 + ½ a (100)
⇒ 500 = 100
⇒ 500 - 100 = 50a
⇒ 400 = 50a
⇒ a = 400/50
⇒ a = 8 m/s2
Step 5: Quote the final answer
Based on the calculation above, the racing car is accelerating at 8 m/s2 north.
Answer : B
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