A car driving along a straight road increases its velocity from 2.8 m/s to 9.7 m/s in 3 seconds. Calculate its acceleration in m/s^2
A skier in the Giant Slalom will accelerate at a constant 5.0 m/s^2 If she starts from rest, how fast is she going after 5 seconds?
A skier at the top of a run will accelerate at a constant 4.0 ft/s^2 If she starts from rest, how far does she travel in 5 seconds?
Please help me with these 3 questions. I am very confused. Thank you.
<<A car driving along a straight road increases its velocity from 2.8 m/s to 9.7 m/s in 3 seconds. Calculate its acceleration in m/s^2 >>
Divide the increase in velocity (9.7-2.8 m/s) by the time interval (3 s)
<<A skier in the Giant Slalom will accelerate at a constant 5.0 m/s^2 If she starts from rest, how fast is she going after 5 seconds? >>
Velocity change = (acceleration) x (time)
<<A skier at the top of a run will accelerate at a constant 4.0 ft/s^2 If she starts from rest, how far does she travel in 5 seconds? >>
Distance travelled = (1/2)(acceleration) t^2
An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.7 km, but when the snow clears, he discovers that he actually traveled 7.8 km at 52° north of due east. how far must he travel to reach base camp?
To solve these questions, we can use the equations of motion that relate displacement, initial velocity, final velocity, acceleration, and time. Here are the steps to find the answers:
1. Calculate acceleration:
Given:
Initial velocity (u) = 2.8 m/s
Final velocity (v) = 9.7 m/s
Time (t) = 3 seconds
Acceleration (a) can be calculated using the equation:
a = (v - u) / t
Substituting the given values:
a = (9.7 - 2.8) / 3
a ≈ 2.3 m/s²
Therefore, the acceleration of the car is approximately 2.3 m/s².
2. Calculate final velocity:
Given:
Acceleration (a) = 5.0 m/s²
Time (t) = 5 seconds
We can use the equation:
v = u + at
Since the skier starts from rest, the initial velocity (u) is 0.
Substituting the given values:
v = 0 + 5.0 * 5
v = 25 m/s
Therefore, after 5 seconds, the skier will be going 25 m/s.
3. Calculate displacement:
Given:
Acceleration (a) = 4.0 ft/s²
Time (t) = 5 seconds
We can use the equation:
s = ut + (1/2)at^2
Since the skier starts from rest, the initial velocity (u) is 0.
Substituting the given values:
s = 0 * 5 + (1/2) * 4.0 * (5^2)
s = 0 + 1/2 * 4.0 * 25
s = 50 ft
Therefore, the skier will travel 50 ft in 5 seconds.
I hope this clears up your confusion. If you have any more questions, feel free to ask!