A competitor is aiming to complete a 1500m wheel-chair race in less than 4 min. After moving at a constant speed for exactly 3.5 min, there were still 240m to go. What must his acceleration be for the remaining distance if he were to finish the race on time?
Well, if he's aiming to finish the race on time, he better put the pedal to the metal! But in this case, since it's a wheel-chair race, I guess he should put the wheels to the track? Anyway, let's calculate the acceleration needed.
We know that the competitor has 240m to go in 30 seconds (4 minutes - 3.5 minutes = 30 seconds). To find the acceleration, we can use the equation:
distance = initial velocity × time + (1/2) × acceleration × time^2
Since the competitor is moving at a constant speed for the first 3.5 minutes, the initial velocity is also the final velocity. We can rewrite the equation as:
240m = v × (30s) + (1/2) × a × (30s)^2
Simplifying that equation, we get:
240m = 30s × v + 15s^2 × a
Now, the competitor still has to cover 240m while maintaining a constant speed, so his final velocity is zero. Plugging that into the equation, we have:
240m = 0 + 15s^2 × a
Simplifying further, we get:
240m = 15s^2 × a
And finally, we can solve for acceleration:
a = 240m / (15s^2)
Now grab your calculator and find that acceleration! And while you're at it, start a clown wheel-chair race. It'll be a fun challenge!
To determine the required acceleration for the remaining distance, we can use the equation for distance traveled with constant acceleration:
d = ut + (1/2)at^2
Where:
- d is the distance traveled,
- u is the initial velocity,
- t is the time, and
- a is the acceleration.
In this case, the distance remaining is 240m, the initial velocity is unknown, the time is 0.5 min (4 min - 3.5 min), and we need to find the acceleration.
Let's label the unknown initial velocity as v.
We know that the distance traveled during the initial 3.5 minutes is given by:
d1 = ut1
where d1 = 1500m - 240m = 1260m (distance traveled in the first 3.5 min) and t1 = 3.5 min.
Now, let's write down the equation for the remaining distance:
240m = vt2 + (1/2)at2^2
where t2 = 0.5 min.
Since the initial velocity is unknown, we can solve for it using the equation for distance traveled during the first 3.5 minutes:
1260m = v(3.5 min)
Simplifying, we find:
v = 1260m / 3.5 min
v = 360 m/min
Now, substitute the values into the equation for the remaining distance:
240m = (360 m/min)(0.5 min) + (1/2)(a)(0.5 min)^2
Simplifying further:
240m = 180 m + 0.125a
Rearranging the equation:
0.125a = 240m - 180m
0.125a = 60m
Dividing both sides by 0.125:
a = 60m / 0.125
a = 480 m/min^2
Therefore, the required acceleration for the remaining distance is 480 m/min^2.
To find the required acceleration for the competitor to finish the race on time, we need to use the equation of motion, specifically the equation that relates displacement, initial velocity, time, and acceleration:
d = ut + (1/2)at^2
where:
d = displacement
u = initial velocity
t = time
a = acceleration
In this case, the displacement is 240m, the initial velocity is the speed of the competitor when there were still 240m to go, which is the same as his constant speed, and the time is the remaining 0.5 minutes (since he has already moved for 3.5 minutes).
Let's start by calculating the initial velocity (u). We know that the constant speed for the competitor is the same as his initial velocity. Since the competitor moved at a constant speed for 3.5 minutes and traveled 1500m, we can calculate the constant speed as:
Speed = distance / time = 1500m / 3.5min
Now, let's calculate the initial velocity (u):
u = Speed = 1500m / 3.5min
Now that we have the initial velocity, let's substitute the values into the equation of motion:
240m = (u * 0.5min) + (1/2)a(0.5min)^2
Simplifying this equation will give us the value of acceleration (a):
240m = (u * 0.5min) + (1/2)a(0.25min^2)
240m = (1500m / 3.5min * 0.5min) + (1/2)a(0.25min^2)
Solving this equation will give us the required acceleration for the competitor to finish the race on time.